All categories

3 years ago

Find the area inside the semicircle and out side the triangle in terms of ń

Mathematics

1 answer:

Elan Coil [88]3 years ago

6 0

Answer:

π 169 / 2 - 120

Step-by-step explanation:

I'm assuming you are asking question about 24.

So first find radius of semicircle:

a^2+b^2=c^2

10^2+24^2=c^2

c=26

radius 26/2 = 13

Then let's calculate area of semicircle

area of circle = π*r^2

area of semicircle = π*r^2 / 2

area of given semi circle = π 169 / 2

Then let's calculate area of triangle

area of triangle = 10 * 24 / 2 = 120

Area of the shaded region = π 169 / 2 - 120

You might be interested in

Pleaseeeee help There was a sample of 200 mg of radioactive substance to start a study. Since then, the sample has decayed by 4.

m_a_m_a [10]

Y=200 (1-0.044)^t
.................

8 0

3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

A rectangle has a length of 12 and a width of 9. What is the

choli [55]

Answer:

Step-by-step explanation:

9 squared + 12 squared

3 0

2 years ago

Write this in words- 2.0120

babymother [125]

Two point zero one hundred twenty

7 0

3 years ago

The function C(t) = 400 + 30t models the number of classrooms, C. in the town of Sirap, t years from

maks197457 [2]

Answer:

1) S(t) = C(t) × D(t)

2) S(t) = (400 + 30t)(25 + t)

Step-by-step explanation:

The function C(t) = 400 + 30t ........... (1), models the number of classrooms, C. in the town of Sirap, t years from now.

The function D(t) = 25 + t ......... (2) models the number of students per classroom, D, t years from now.

Then if S(t) represents the number of students in Sirap's school system t years from now, then, we can write the relation

1) S(t) = C(t) × D(t) (Answer)

2) Hence, the formula of S(t) in terms if t is given by

S(t) = (400 + 30t)(25 + t) (Answer)

7 0

3 years ago

Read 2 more answers